Elastic composites are commonly incorporated into products (e.g., diapers, training pants, garments, etc.) to improve their ability to better fit the contours of the body. For example, the elastic composite may be formed from an elastic film and one or more nonwoven web materials. The nonwoven web material may be joined to the elastic film while the film is in a stretched condition so that the nonwoven web material can gather between the locations where it is bonded to the film when it is relaxed. The resulting elastic composite is stretchable to the extent that the nonwoven web material gathered between the bond locations allows the elastic film to elongate. Unfortunately, elastic films often have unpleasant tactile aesthetic properties, such as feeling rubbery or tacky to the touch, making them unpleasant and uncomfortable against the wearer's skin. In an effort to improve these properties, attempts have been made to aperture the composite. For example, U.S. Pat. No. 6,830,800 to Curro, et al. describes a method in which an elastic material is joined between two webs. The elastic material is apertured in regions coincident the bond sites so that the first and second webs are joined through the apertures. Despite the benefits achieved, however, a need for improvement nevertheless remains.